# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:![X4]:s(t_h4s_options_option(X3),h4s_options_optionu_u_map2(s(t_fun(X1,t_fun(X2,X3)),X4),s(t_h4s_options_option(X1),h4s_options_none),s(t_h4s_options_option(X2),h4s_options_none)))=s(t_h4s_options_option(X3),h4s_options_none),file('i/f/option/OPTION__MAP2__THM_c3', ch4s_options_OPTIONu_u_MAP2u_u_THMu_c3)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/option/OPTION__MAP2__THM_c3', aHLu_TRUTH)).
fof(3, axiom,~(p(s(t_bool,f0))),file('i/f/option/OPTION__MAP2__THM_c3', aHLu_FALSITY)).
fof(4, axiom,![X5]:(s(t_bool,X5)=s(t_bool,t)|s(t_bool,X5)=s(t_bool,f0)),file('i/f/option/OPTION__MAP2__THM_c3', aHLu_BOOLu_CASES)).
fof(10, axiom,![X3]:s(t_bool,h4s_options_isu_u_some(s(t_h4s_options_option(X3),h4s_options_none)))=s(t_bool,f0),file('i/f/option/OPTION__MAP2__THM_c3', ah4s_options_ISu_u_SOMEu_u_DEFu_c1)).
fof(11, axiom,![X1]:![X2]:![X3]:![X7]:![X6]:![X4]:?[X8]:((p(s(t_bool,X8))<=>(p(s(t_bool,h4s_options_isu_u_some(s(t_h4s_options_option(X1),X6))))&p(s(t_bool,h4s_options_isu_u_some(s(t_h4s_options_option(X2),X7))))))&s(t_h4s_options_option(X3),h4s_options_optionu_u_map2(s(t_fun(X1,t_fun(X2,X3)),X4),s(t_h4s_options_option(X1),X6),s(t_h4s_options_option(X2),X7)))=s(t_h4s_options_option(X3),h4s_bools_cond(s(t_bool,X8),s(t_h4s_options_option(X3),h4s_options_some(s(X3,happ(s(t_fun(X2,X3),happ(s(t_fun(X1,t_fun(X2,X3)),X4),s(X1,h4s_options_the(s(t_h4s_options_option(X1),X6))))),s(X2,h4s_options_the(s(t_h4s_options_option(X2),X7))))))),s(t_h4s_options_option(X3),h4s_options_none)))),file('i/f/option/OPTION__MAP2__THM_c3', ah4s_options_OPTIONu_u_MAP2u_u_DEF)).
fof(12, axiom,![X3]:![X6]:s(t_bool,h4s_options_isu_u_some(s(t_h4s_options_option(X3),h4s_options_some(s(X3,X6)))))=s(t_bool,t),file('i/f/option/OPTION__MAP2__THM_c3', ah4s_options_ISu_u_SOMEu_u_DEFu_c0)).
fof(16, axiom,![X3]:![X12]:![X13]:s(X3,h4s_bools_cond(s(t_bool,f0),s(X3,X13),s(X3,X12)))=s(X3,X12),file('i/f/option/OPTION__MAP2__THM_c3', ah4s_bools_CONDu_u_CLAUSESu_c1)).
# SZS output end CNFRefutation
